Simplify the following expression: $\dfrac{66r^3}{88r}$ You can assume $r \neq 0$.
Answer: $ \dfrac{66r^3}{88r} = \dfrac{66}{88} \cdot \dfrac{r^3}{r} $ To simplify $\frac{66}{88}$ , find the greatest common factor (GCD) of $66$ and $88$ $66 = 2 \cdot 3 \cdot 11$ $88 = 2 \cdot 2 \cdot 2 \cdot 11$ $ \mbox{GCD}(66, 88) = 2 \cdot 11 = 22 $ $ \dfrac{66}{88} \cdot \dfrac{r^3}{r} = \dfrac{22 \cdot 3}{22 \cdot 4} \cdot \dfrac{r^3}{r} $ $\phantom{ \dfrac{66}{88} \cdot \dfrac{3}{1}} = \dfrac{3}{4} \cdot \dfrac{r^3}{r} $ $ \dfrac{r^3}{r} = \dfrac{r \cdot r \cdot r}{r} = r^2 $ $ \dfrac{3}{4} \cdot r^2 = \dfrac{3r^2}{4} $